This clinical trial is being developed to treat patients with advanced Merkel cell carcinoma (stage 3b or 4) off-label with the FDA-approved drug ipilimumab at the NIH Clinical Research Center and other study sites. The manufacturer is supplying the drug and a final agreement regarding the clinical trial is being negotiated with them. The trial protocol has been developed and has been approved by the NCI IRB. Patients will be treated with ipilimumab and followed to monitor clinical response. In addition, tumor specimens and blood will be collected to evaluate anti-tumor immune responses during treatment.